Progress in FY 2004 has been in the following areas: (1) We have continued structural studies of amyloid fibrils. We have determined a number of tertiary contacts in amyloid fibrils formed by the Alzheimer's beta-amyloid peptide, using new solid state NMR methods. This allows us to refine our structural model for beta-amyloid fibrils, which was published in 2002. We have identified a number of specific differences in tertiary contacts and supramolecular structure between beta-amyloid fibrils with significantly different morphologies, providing support for the hypothesis that different amyloid polymorphs have different structures at the molecular-level, which may account for biomedical phenomena such as prion strains. (2) We have carried out initial structural studies of a 40-residue peptide from HIV-1 Vpu, containing its transmembrane segment, in phospholipid bilayers. These data allow us to identify the transmembrane segment and the relative mobility of extramembrane segments. We have developed an expression and purification protocol for full-length Vpu that will permit future solid state NMR studies of its structure in bilayers. (3) We have completed solid state NMR measurements on the model helical protein HP35 under chemical denaturation. These measurements have important implications for the understanding of protein folding phenomena, showing that the unfolded state is not a uniform random coil, and that intermediate states in thermodynamic unfolding can not be described accurately by a simple two-state model. (4) We have developed new solid state NMR methods, including methods for measuring specific carbon-carbon distances in uniformly carbon-13-enriched samples, methods for extracting structural constraints from solid state NMR spectra of amyloid fibrils aligned on planar substrates, and a new form of two-dimensional solid state NMR spectroscopy (based on transverse magnetization exchange) with improved sensitivity.